Retail Math Equations for the Apparel Industry

Please utilize these fashion retail math formulas at your own risk.  The Apparel Search Company is "not" comprised of mathematicians.  We have simply listed formulas that we have collected over the years.  In addition, we have supplemented the listing with information that we have received from our viewers.  If you have additional formulas or you think any of the above formulas are incorrect, please let us know.

\$ Cost

Cost of Goods Sold (COGS)

\$ Retail

\$ Markdown

GMROI

Gross Margin

Markdown \$

Markup

Margin %

Markup cancellation

Percent change in sales

Planned Stock

Profit Margin

Sell Through %

Stock Sales Ratio

Shrinkage

Turnover

Breakeven Analysis

Weeks of Stock

You may also want to learn about retail store assortment planning from our fashion terms section.

Help us improve; you can e-mail additional formulas or good examples to go with our formulas to us from our contact page.

\$ Cost =  \$ Retail  x  (100% - Markup %)

Cost of Goods Sold (COGS)
=  Beginning Inventory  +  Purchases - End Inventory

The above formula is an example of a company that sells finished goods. The formula can be applied to one week, one month or a year, but must be the same for each value of the formula. The formula for a manufacturer includes raw goods and unfinished product in inventory.  There is no formula for a service firm, which relies exclusively on market research of competitors and deciding a pricing strategy that allows profitability.

Here is another way of stating the same formula:

inventory at beginning of year + purchases or additions during the year = goods available for sale - inventory at end of year = cost of goods sold

\$ Retail
=  \$ Cost / (100% - markup %)

\$ Markdown
=  Original retail price - lower retail price

GMROI
(Gross Margin Return On Investment) =  (GM% x turnover) / (1 - markup %)

an example of how to calculate ones return on investment, (ROI).

Last August the stores sales were \$ 1,814,476, beginning inventory was 4,875,911, and ending inventory was 4,693,452. August maintained a mark-up of 28%.

The formula for reaching the ROI in this scenario would be as follows.

Last Years August sales \$1,814,476  x  28% =  \$508,053.28

Beginning Inventory \$4,875,911 + Ending Inventory  4,693,452  = 9,569,363 divided by 2 = 4,784,681

508,053.28 divided by 4,784,691.5 = 10.6 % ROI (Return on Investment)

Gross Margin =  Sales - cost of good sold

Margin %  =  (\$ Retail - \$ Cost) / \$ Retail

Markdown % =  \$ Markdown  /  \$ Net Sales

Markup =  The difference between the cost of an item and its selling price.

Markup cancellation =  Reduction from original markup %

You can calculate the percent of change (percent of increase or percent of decrease) from the following formula.

This Period of Sales  - Last Period of Sales / Last Period of Sales x100% = percent of Change

Example, Apparel Search sold \$1500. worth of blue shirts last year.  This year we sold \$1575. worth of blue shirts.   What is the percent of increase on the blue shirts we sold?

(\$1575 - \$1500) / \$1500 x100% =  5%

The increase was 5%

Example, A shirt on ApparelSearch.com is sold at a 20% discount off the original price of \$32.    What is the Sales Price?

Let the sales price by "x" dollars.

(\$32 - X) / \$32 x 100% = 20%

(\$32 -X) / \$32 = 0.2

\$32-X = \$6.4

X = \$25.6

Therefore,  the sales price of the shirt is \$25.60

Example, The original price of a leather jacket was \$500.  It is now on sale for \$440.  What is the percent of decrease?

Let "X" be the percent of decrease.

X/100 = (500-440)/500
500X = 6000
X= 12

Therefore, there was a 12% decrease.

Planned Stock  = planned monthly sales x stock sales ratio

Sell through % = units sold / (units sold + on hand inventory)

Sell-through is a percentage of units sold during a period (for example 1 month).

It is calculated by dividing the number of units sold by the beginning on-hand inventory (for that same time period).

Example:

During the month of August you sell 100 shirts. You received 300 shirts in receipts. You end August with 900 units shirts of stock (End of Month Stock).  What was your Beginning On-Hand units of shirts and what was your Sell-through?

Beginning of Month stock (BOM) = EOM 900 units - Receipts 300 units + Sales 100 units = 700 units

Sell-through = Sales 100 units / Beginning Inventory (BOM) 700 = 14.3% Sell-through in August.

• Sell-through % Is a percentage of units sold during a period and it is calculated by dividing the number of units sold by the beginning on-hand inventory (for that same time period).

BOM means Beginning of Month
EOM means End of Month

Stock Sales Ratio =  B.O.M. \$ Stock / Sales for period

Note:  B.O.M = beginning of month

Shrinkage =  Difference between book and physical inventory

"inventory turnover." Turnover is the number of times you sell your average investment in inventory each year.

Turnover  = net sales for period / average stock for period

Here is another way of stating the same formula:

Cost of Goods Sold from Stock Sales during the Past 12 Months
Average Inventory Investment during the Past 12 Months

Inventory turns: The retail sales for a period divided by the average inventory value for that period. Most retailers are in the range of two to four turns a year.

Average Stock  =   sum of each periods Beginning of Period stock  +  the last End of Period stock / # of periods

Breakeven = Fixed Costs / (Revenue
Variable Costs)

Breakeven Analysis:  Simply stated, this formula indicates how much sales volume must be accomplished in order to cover all costs (fixed and variable), and begin generating a profit.  In other words, it is the point in sales volume at which you have no profit and no loss. This is most commonly applied to a business that sells product.

Weeks of Stock

Inventory divided by average weekly sales for a given period of time.

If you have \$10,000. worth of inventory in sweaters, and your total sales of sweaters for the past 5 weeks is \$20,000. the calculation would look as below:

\$20,000 divided by 5 = average weekly sales of \$4,000.

\$10,000. divided by \$4,000.00 = 2.5

This means that if you did not replenish your sweater inventory and sales continued at the same rate, you would deplete your inventory of sweaters to zero within 2 1/2 weeks.

By the way, what are the odds that the your inventory would sell at the "same rate" week after week.  Maybe this is why clothing stores are always out of my size.

If you do not find enough on this page, you can find books about retail math in the Math for Merchandising Books section.

Please utilize these formulas at your own risk.  The Apparel Search Company is "not" comprised of mathematicians.  We have simply listed formulas that we have collected over the years.  In addition, we have supplemented the listing with information that we have received from our viewers.   If you have additional formulas or you think any of the above formulas are incorrect, please contact us.

If you are a clothing retailer and you have retail math formulas that are not listed on this page, PLEASE let us know them so we can make this section more complete.